This invention relates to generation of code signals, such as pseudo-noise signals, and more particularly to a method for generating families of orthogonal and pseudo-orthogonal codes and code-modulated waveforms. The codes can be used in a variety of applications including, but not limited to, communication systems such as spread spectrum communication systems, encryption of data, pictures, and audio, and the generation of signals for radar applications.
Pseudo-noise codes are used in various applications, including those listed above. So-called xe2x80x9cspread spectrumxe2x80x9d communication uses noise-like carrier waves, and a bandwidth that is much wider than conventional point-to-point communication at the same data rate. Among the advantages are: excellent noise immunity, relatively low power consumption, and reduction or elimination of the effects of multipath fading. Code division multiple access (xe2x80x9cCDMAxe2x80x9d) is a form of spread spectrum that has gained popular acceptance by cellular radio system operators as a technique that increases system capacity and service quality. Different users can occupy the same communication channel; this being achieved by assigning to each user a distinctive pseudo-noise code that can be recognized by the intended user but is, ideally, received as noise by the other users.
The ability to quickly generate families of pseudo-noise codes with minimal computation and cost is very advantageous for the described types of applications, but has been difficult to achieve in the prior art. Accordingly, it is among the objects of the present invention to provide a method and apparatus for efficiently generating families of pseudo-noise codes and code signals.
The present invention employs a multi-scale shuffle in the generation of orthogonal and pseudo-orthogonal codes. Interleaving operations are used that are of a type related to so-called xe2x80x9cFinite Gelfand Pairsxe2x80x9d.
In accordance with an embodiment of the invention, a method is provided for generating a family of pseudo-random orthogonal or pseudo-orthogonal code signals, comprising the following steps: generating a seed matrix of original dimensions; performing a plurality of expansions on the seed matrix, each successive expansion producing a next generation matrix of larger dimensions, the last of the expansions producing a final matrix; at least some of the expansions including replication and shuffling of a parent generation matrix to produce a child generation matrix; and outputting rows of the final matrix as the family of code signals.
In a preferred embodiment of the invention, the shuffling comprises a pseudo-random re-ordering of matrix column indices. In a form of this embodiment, the replication and shuffling comprises forming a child generation matrix by operations that include combining a reproduction of the parent matrix and a shuffled reproduction of the parent matrix. In another form of this embodiment, the replication and shuffling comprises forming an intermediate matrix by operations that include combining a reproduction of the parent matrix, a modified reproduction of the parent matrix, a shuffled reproduction of the parent matrix, and a modified shuffled reproduction of the parent matrix, and then shuffling the intermediate matrix to form the child matrix.
The code generation hereof has several advantages, among which are the following: (1) The codes have additive white Gaussian white noise (AWGN) statistics and present ideal noise-like auto- and cross-correlation properties. (2) The codes exhibit full non-linearity; that is, the codes are not generated with linear transformations, such as shift-register sequences or Gold-codes. This enhances their use for covert-comm applications. (3) The codes have the property of non-detectability; that is an overlayed version of the codes is non-detectable in the sense of Knuth""s R4 property. (4) Flexibility is provided in the choice of the number of phases. The codes can be chosen to have any number 2xc2x7n phases to adapt to different applications, and do not have to be quantized in order to be implemented. This results in a better performance at the auto- and cross-correlation level. (5) The technique hereof provides fast generation. The complete frame of N multiscale codes of length N requires only Nxc2x7log N computations, for any number of phases.
Further features and advantages of the invention will become more readily apparent from the following detailed description when taken in conjunction with the accompanying drawings.